Least Common Multiple of 7208 and 7214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7208 and 7214 the smallest integer that is 25999256 that is divisible by both numbers.

Least Common Multiple (LCM) of 7208 and 7214 is 25999256.

LCM(7208,7214) = 25999256

LCM of 7208 and 7214

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 7208 and 7214

LCM of 7208 and 7214 is 25999256

Least common multiple can be found by multiplying the highest exponent prime factors of 7208 and 7214. First we will calculate the prime factors of 7208 and 7214.

Prime Factorization of 7208


2 7208
2 3604
2 1802
17 901
53 53
1

Prime factors of 7208 are 2, 17,53. Prime factorization of 7208 in exponential form is:

7208 = 23×171×531

Prime Factorization of 7214


2 7214
3607 3607
1

Prime factors of 7214 are 2,3607. Prime factorization of 7214 in exponential form is:

7214 = 21×36071

Now multiplying the highest exponent prime factors to calculate the LCM of 7208 and 7214.

LCM(7208,7214) = 23×171×531×36071
LCM(7208,7214) = 25999256

Factors of 7208

List of positive integer factors of 7208 that divides 7208 without a remainder.

1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208

Factors of 7214

List of positive integer factors of 7214 that divides 7214 without a remainder.

1, 2, 3607, 7214

Least Common Multiple of 7208 and 7214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7208 and 7214, than apply into the LCM equation.

GCF(7208,7214) = 2
LCM(7208,7214) = ( 7208 × 7214) / 2
LCM(7208,7214) = 51998512 / 2
LCM(7208,7214) = 25999256

Properties of LCM 7208 and 7214

(i) The LCM of 7214 and 7208 is associative

LCM of 7208 and 7214 = LCM of 7214 and 7208

Related Least Common Multiples of 7208

Related Least Common Multiples of 7214

Frequently Asked Questions on LCM of 7208 and 7214

1. What is the LCM of 7208 and 7214?

Answer: LCM of 7208 and 7214 is 25999256.

2. What are the Factors of 7208?

Answer: Factors of 7208 are 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208. There are 16 integers that are factors of 7208. The greatest factor of 7208 is 7208.

3. What are the Factors of 7214?

Answer: Factors of 7214 are 1, 2, 3607, 7214. There are 4 integers that are factors of 7214. The greatest factor of 7214 is 7214.

4. How to Find the LCM of 7208 and 7214?

Answer:

Least Common Multiple of 7208 and 7214 = 25999256

Step 1: Find the prime factorization of 7208

7208 = 2 x 2 x 2 x 17 x 53

Step 2: Find the prime factorization of 7214

7214 = 2 x 3607

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 25999256 = 2 x 2 x 2 x 17 x 53 x 3607

Step 4: Therefore, the least common multiple of 7208 and 7214 is 25999256.